Complex Network Theory – An Introduction

gooseliverBiotechnology

Oct 22, 2013 (3 years and 9 months ago)

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Complex Network Theory


An
Introduction

Niloy Ganguly

Complex systems

Made of
many non
-
identical
elements

connected by diverse
interactions
.

NETWORK

Business ties in US biotech
-
industry

Nodes: companies:
investment


pharma


research labs


public


biotech
nology



Links:
financial


R&D collaborations

http://ecclectic.ss.uci.edu/~drwhite/Movie

Business ties in US biotech
-
industry

Nodes: companies:
investment


pharma


research labs


public


biotech
nology



Links:
financial


R&D collaborations

http://ecclectic.ss.uci.edu/~drwhite/Movie

Red
,
blue
, or
green
: departments

Yellow
: consultants

Grey
: external experts

Structure of an organization

www.orgnet.com

Internet

Friendship Network

Network Collaboration Network

9
-
11 Terrorist (?) Network


Social Network Analysis is a
mathematical methodology for
connecting the dots

--

using
science to fight terrorism.
Connecting multiple pairs of
dots soon reveals an emergent
network

of organization.

Swedish sex
-
web

Nodes:

people (Females; Males)

Links:

sexual relationships

Liljeros et al.
Nature

2001

4781 Swedes; 18
-
74;

59% response rate.

Road and Airlines Network

-

-

Genetic interaction network

Yeast protein
-
protein interaction network

What Questions can be asked


Does these networks display some
symmetry


Are these networks creation of intelligent
objects or they have emerged.


How have these networks emerged


Underlying simple rules leading to their complex
formation

What Questions can be asked


Can we predict some outcomes/ make
statements about the health of the system
represented by the network


Are these networks robust against failure


Does these networks help in information
flow


How can we engineer (build) such network,
(engineering complex systems).

Symmetry

Poisson distribution

Exponential Network

Power

-

law distribution

Scale

free Network

Friendship Network (Community)

Karate Club

Instructors 1 and 33

The Small World Effect

Even in very large social networks, the average distance between
nodes is usually quite short.


Milgram’s small world experiment:


Target individual in Boston


Initial senders in Omaha, Nebraska


Each sender was asked to forward a packet to a friend who was
closer to the target


Friends asked to do the same

Result: Average of ‘six degrees’ of separation.


S. Milgram,
The small world problem,
Psych. Today, 2 (1967), pp. 60
-
67
.



The Small World Effect

Watts
-
Strogatz ‘Small World’ Model
(Simple Rules)

Watts and Strogatz introduced this simple model to show how
networks can have both short path lengths and high clustering.

D. J. Watts and S. H. Strogatz,

Collective dynamics of “small
-
world”
networks
, Nature, 393 (1998), pp. 440

442.


Swedish sex
-
web

Nodes:

people (Females; Males)

Links:

sexual relationships

Liljeros et al.
Nature

2001

4781 Swedes; 18
-
74;

59% response rate.

Swedish sex
-
web

Nodes:

people (Females; Males)

Links:

sexual relationships

Liljeros et al.
Nature

2001

4781 Swedes; 18
-
74;

59% response rate.

Internet


Robust against random failure


Vulnerable against attack

9
-
11 Terrorist (?) Network



How to conduct investigation

Some interesting Problems


Consonants (Language) Networks


Marriage Networks


Collaboration Networks


Build Networks which are robust as well as
efficient


Actors Network

Course Outline


Techniques to analyze networks


Special types of networks


random
networks, power law networks, small world
networks


Models of network growth


Processes taking place on network


search,
epidemics


Case Study



Traditional vs. Complex Systems
Approaches to Networks

Traditional Questions:

Social Networks:

Who is the most
important person in
the network?

Graph Theory:

Does there exist a cycle
through the network that
uses each edge exactly
once?

Complex Systems Questions:

What fraction of edges have to be removed to
disconnect the graph?


What kinds of structures emerge from simple
growth rules?